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Ehresmann's lemma

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In mathematics, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping , where and are smooth manifolds, is

  1. a surjective submersion, and
  2. a proper map (in particular, this condition is always satisfied if M is compact),

then it is a locally trivial fibration. This is a foundational result in differential topology due to Charles Ehresmann, and has many variants.

See also

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References

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  • Ehresmann, Charles (1951), "Les connexions infinitésimales dans un espace fibré différentiable", Colloque de topologie (espaces fibrés), Bruxelles, 1950, Georges Thone, Liège; Masson et Cie., Paris, pp. 29–55, MR 0042768
  • Kolář, Ivan; Michor, Peter W.; Slovák, Jan (1993). Natural operations in differential geometry. Berlin: Springer-Verlag. ISBN 3-540-56235-4. MR 1202431. Zbl 0782.53013.